[Linear Algebra] Eigenvector & Eigenvalue

Eigenvalue, Eigenvector, Eigenspace

(A-λI)T

Characteristic polynomial

det(A-λI) = 0을 만족하는 λ가 A의 eigenvalue이다.
det(A-λI) = 0를 characteristic equation이라 한다.

Similarity

Diagonalizable

square matrix A가 diagonal matrix와 similar하면, diagonalizable이라 한다.
A = PDP-1, D는 diagonal matrix

Theorem. The Diagonalization Theorem

Diagonalization

Eigenvectors & Linear Transformation